M2918231 Mersenne number exponent details

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M2918231

<<<

>>>

is 2 ^2918231 - 1

has 878476 decimal digits

takes 0.225 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	A46F1BAFFEA76AFE	double-checked
PRP	C721BA31451CC49E	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.4250	67.6471%	5000000	200000000	1.7498	9.1933%	22.1748	70.6214%	2.9743%
PrimeNet	2⁵⁹	0.0263	62.7119%	13000	260000	0.0030	3.0677%	0.0293	63.8558%	1.1439%
GPU72	2⁶³	0.5469	65.0794%	17000	300000	0.0036	1.9437%	0.5505	65.7581%	0.6787%
Difference	+5	+19.8781	+2.5677%	+4983000	+199700000	+1.7462	+7.2496%	+21.6242	+4.8633%	+4.8633%

Known prime factors (1 factor, 76.2 bits, 0.00261099% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2918231	86469621470970519242177	23	76.195	14815417537366048 2⁵ × 462981798042689	2021-01-30	32	462981798042689	6,365.8	2,824,954	5,276,228

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.246%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.145%
2010-11-13T11:54:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.213%
2010-11-15T11:28:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.582%
2015-04-27T09:55:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.228	-	-	5.537%
2020-04-02T14:02:20	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.193%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:24	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.053	-	-
2009-02-14T12:28:00	Sturle Sunde	krebs.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2011-12-22T07:14:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-10T21:10:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.336	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.673	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.280	-	-
2016-02-22T09:35:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.561	-	-
2017-11-19T23:57:51	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.121	-	-
2018-12-18T01:52:41	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.24	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.664 GHz-days
Estimated T-Level:	2.700

Digits	B1	Curves	Complete	FacMiss
20	11000	54 / 100	0.540	58.117%
25	50000	54 / 280	0.193	82.432%

New Calculation Method

Total ECM effort:	5.664 GHz-days
Estimated T-Level:	2.700

Digits	B1	Complete	FacMiss
20	11000	1.742	17.518%
25	50000	0.157	85.433%
30	250000	0.010	99.035%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		53	5.559
50000	5000000	86469621470970519242177	1	0.105

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-28T12:10:00	Smurgs	Praca	50000	5000000						3	0.315
2011-03-30T12:26:00	S00030	op9020-usff	50000	5000000						3	0.315
2013-06-07T03:11:00	ANONYMOUS		50000	5000000						3	0.315
2015-12-24T22:56:25	Bruce	Desk7	50000	5000000						3	0.315
2016-09-19T14:59:31	Bruce	test	50000	5000000						3	0.315
2019-07-29T14:16:47	Claude Portenier	Petit-Idiot	50000	5000000						3	0.315
2020-08-19T05:51:31	daveward2005	Davy	50000	5000000						7	0.734
2020-09-23T11:49:13	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						7	0.734
2020-10-19T17:33:47	mnd9	50871	50000	5000000						7	0.734
2020-11-23T10:24:56	GAN	AC-GR	50000	5000000						7	0.734
2020-12-29T16:12:26	RIHATEC	i7-3770K	50000	5000000						7	0.734
2021-01-30T06:19:45	mnd9	office2	50000	5000000	86469621470970519242177	76.195	1	2	8463676541580644	1	0.105

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	Choi4KANG	v4_computers	A46F1BAFFEA76AFE	0.225
2018-10-04T20:04:23	kkmrkkblmbrbk	old	A46F1BAFFEA76AFE	0.225

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-30T22:25:29

mrh

86469621470970519242177

C721BA31451CC49E

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

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10³

10⁴

10⁵

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10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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10¹⁵

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-01-30T22:25:29+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront